Elliptic curves over $\Q$ of conductor 143344

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
143344.a1	143344l2	143344.a	143344l	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{11} \cdot 17^{6} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$248$	$12$	$0$	$1.769456718$	$1$		$3$	$294912$	$1.315947$	$1825346/961$	$0.88772$	$3.28823$	$[0, 1, 0, -9344, 101332]$	\(y^2=x^3+x^2-9344x+101332\)	2.3.0.a.1, 8.6.0.b.1, 124.6.0.?, 248.12.0.?	$[(164, 1734)]$	$1$
143344.a2	143344l1	143344.a	143344l	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{10} \cdot 17^{6} \cdot 31 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$248$	$12$	$0$	$3.538913436$	$1$		$3$	$147456$	$0.969374$	$48668/31$	$0.79741$	$2.92458$	$[0, 1, 0, 2216, 13476]$	\(y^2=x^3+x^2+2216x+13476\)	2.3.0.a.1, 8.6.0.c.1, 62.6.0.b.1, 248.12.0.?	$[(66, 672)]$	$1$
143344.b1	143344m1	143344.b	143344m	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{6} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1.214415332$	$1$		$2$	$73728$	$0.613286$	$-256/31$	$0.78373$	$2.58278$	$[0, 1, 0, -96, -5309]$	\(y^2=x^3+x^2-96x-5309\)	62.2.0.a.1	$[(45, 289)]$	$1$
143344.c1	143344a1	143344.c	143344a	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{14} \cdot 17^{9} \cdot 31^{2} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.3	2B	$136$	$12$	$0$	$1$	$1$		$1$	$2924544$	$2.354820$	$801765089/3844$	$0.86422$	$4.57500$	$[0, 1, 0, -1521392, 718781908]$	\(y^2=x^3+x^2-1521392x+718781908\)	2.3.0.a.1, 8.6.0.e.1, 34.6.0.a.1, 136.12.0.?	$[ ]$	$1$
143344.c2	143344a2	143344.c	143344a	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{13} \cdot 17^{9} \cdot 31^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.3	2B	$136$	$12$	$0$	$1$	$4$	$2$	$1$	$5849088$	$2.701393$	$-90518849/1847042$	$0.92434$	$4.69371$	$[0, 1, 0, -735312, 1461155860]$	\(y^2=x^3+x^2-735312x+1461155860\)	2.3.0.a.1, 8.6.0.e.1, 68.6.0.c.1, 136.12.0.?	$[ ]$	$1$
143344.d1	143344b1	143344.d	143344b	$2$	$3$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{6} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$6324$	$16$	$0$	$5.146237371$	$1$		$0$	$110592$	$0.644845$	$-87808/31$	$0.69864$	$2.66412$	$[0, 1, 0, -674, -8777]$	\(y^2=x^3+x^2-674x-8777\)	3.4.0.a.1, 62.2.0.a.1, 186.8.0.?, 204.8.0.?, 6324.16.0.?	$[(2519/5, 122247/5)]$	$1$
143344.d2	143344b2	143344.d	143344b	$2$	$3$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{6} \cdot 31^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$6324$	$16$	$0$	$1.715412457$	$1$		$2$	$331776$	$1.194151$	$38112512/29791$	$0.88754$	$3.13551$	$[0, 1, 0, 5106, 84859]$	\(y^2=x^3+x^2+5106x+84859\)	3.4.0.a.1, 62.2.0.a.1, 186.8.0.?, 204.8.0.?, 6324.16.0.?	$[(895, 26877)]$	$1$
143344.e1	143344n1	143344.e	143344n	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{7} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1054$	$2$	$0$	$4.987157628$	$1$		$0$	$82944$	$0.902836$	$-4000000/527$	$0.73553$	$2.96292$	$[0, -1, 0, -2408, -49601]$	\(y^2=x^3-x^2-2408x-49601\)	1054.2.0.?	$[(4601/4, 306629/4)]$	$1$
143344.f1	143344c1	143344.f	143344c	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{9} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1054$	$2$	$0$	$13.05408448$	$1$		$0$	$274176$	$1.321491$	$256/31$	$0.67265$	$3.29785$	$[0, -1, 0, 1638, -368657]$	\(y^2=x^3-x^2+1638x-368657\)	1054.2.0.?	$[(417517/33, 270049715/33)]$	$1$
143344.g1	143344o1	143344.g	143344o	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{8} \cdot 31 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$165888$	$1.102037$	$-9199872/8959$	$0.70384$	$3.09891$	$[0, 0, 0, -3179, -112999]$	\(y^2=x^3-3179x-112999\)	62.2.0.a.1	$[ ]$	$1$
143344.h1	143344p1	143344.h	143344p	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{12} \cdot 31 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$6137856$	$2.718925$	$-2665856613954845952/748264639$	$1.02878$	$5.23869$	$[0, 0, 0, -21036599, -37137401391]$	\(y^2=x^3-21036599x-37137401391\)	62.2.0.a.1	$[ ]$	$1$
143344.i1	143344d1	143344.i	143344d	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{6} \cdot 31 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$124416$	$0.857618$	$-33958656/31$	$1.22690$	$3.12592$	$[0, 0, 0, -4913, 132651]$	\(y^2=x^3-4913x+132651\)	62.2.0.a.1	$[ ]$	$1$
143344.j1	143344e2	143344.j	143344e	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{17} \cdot 17^{8} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.6	2B	$4216$	$12$	$0$	$2.687128333$	$1$		$3$	$2211840$	$2.235104$	$450335804625/8887328$	$0.90500$	$4.39234$	$[0, 0, 0, -738395, -240019702]$	\(y^2=x^3-738395x-240019702\)	2.3.0.a.1, 8.6.0.b.1, 2108.6.0.?, 4216.12.0.?	$[(12733, 1433440)]$	$1$
143344.j2	143344e1	143344.j	143344e	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{22} \cdot 17^{7} \cdot 31 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.1	2B	$4216$	$12$	$0$	$5.374256666$	$1$		$3$	$1105920$	$1.888531$	$3375/539648$	$1.11262$	$3.87185$	$[0, 0, 0, 1445, -11113206]$	\(y^2=x^3+1445x-11113206\)	2.3.0.a.1, 8.6.0.c.1, 1054.6.0.?, 4216.12.0.?	$[(271, 3030)]$	$1$
143344.k1	143344f1	143344.k	143344f	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{28} \cdot 17^{9} \cdot 31^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.3.82	2B	$16864$	$384$	$21$	$1$	$1$		$1$	$33423360$	$3.934322$	$777228872334890625/60523872256$	$1.08384$	$6.31780$	$[0, 0, 0, -1505711675, 22487005115498]$	\(y^2=x^3-1505711675x+22487005115498\)	2.3.0.a.1, 4.12.0.f.1, 8.24.0.bt.1, 16.48.1.ch.1, 32.96.3.bs.1, $\ldots$	$[ ]$	$1$
143344.k2	143344f2	143344.k	143344f	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{20} \cdot 17^{9} \cdot 31^{8} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.3.230	2B	$16864$	$384$	$21$	$1$	$4$	$2$	$1$	$66846720$	$4.280891$	$-631595585199146625/218340105584896$	$1.07373$	$6.33977$	$[0, 0, 0, -1405093435, 25621685888106]$	\(y^2=x^3-1405093435x+25621685888106\)	2.3.0.a.1, 4.6.0.e.1, 8.24.0.bi.1, 16.48.1.bl.1, 32.96.3.bh.1, $\ldots$	$[ ]$	$1$
143344.l1	143344g1	143344.l	143344g	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{28} \cdot 17^{3} \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.3.82	2B	$16864$	$384$	$21$	$2.866230765$	$1$		$3$	$1966080$	$2.517715$	$777228872334890625/60523872256$	$1.08384$	$4.88604$	$[0, 0, 0, -5210075, 4577041546]$	\(y^2=x^3-5210075x+4577041546\)	2.3.0.a.1, 4.12.0.f.1, 8.24.0.bt.1, 16.48.1.ch.1, 32.96.3.bs.1, $\ldots$	$[(1407, 5642)]$	$1$
143344.l2	143344g2	143344.l	143344g	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{20} \cdot 17^{3} \cdot 31^{8} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	32.96.3.230	2B	$16864$	$384$	$21$	$5.732461530$	$1$		$1$	$3932160$	$2.864288$	$-631595585199146625/218340105584896$	$1.07373$	$4.90801$	$[0, 0, 0, -4861915, 5215079562]$	\(y^2=x^3-4861915x+5215079562\)	2.3.0.a.1, 4.6.0.e.1, 8.24.0.bi.1, 16.48.1.bl.1, 32.96.3.bh.1, $\ldots$	$[(34127/7, 15966054/7)]$	$1$
143344.m1	143344h4	143344.m	143344h	$4$	$4$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{13} \cdot 17^{6} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$4216$	$48$	$0$	$1$	$16$	$2$	$1$	$884736$	$2.001675$	$3999236143617/62$	$1.07559$	$4.57628$	$[0, 0, 0, -1529099, -727782342]$	\(y^2=x^3-1529099x-727782342\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 136.24.0.?, 248.24.0.?, $\ldots$	$[ ]$	$1$
143344.m2	143344h3	143344.m	143344h	$4$	$4$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{13} \cdot 17^{6} \cdot 31^{4} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.15	2B	$4216$	$48$	$0$	$1$	$1$		$1$	$884736$	$2.001675$	$3196010817/1847042$	$1.17908$	$3.97559$	$[0, 0, 0, -141899, 756602]$	\(y^2=x^3-141899x+756602\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.k.1, 68.12.0-4.c.1.2, 136.24.0.?, $\ldots$	$[ ]$	$1$
143344.m3	143344h2	143344.m	143344h	$4$	$4$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{14} \cdot 17^{6} \cdot 31^{2} \)	$0$	$\Z/2\Z\oplus\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.3	2Cs	$4216$	$48$	$0$	$1$	$4$	$2$	$3$	$442368$	$1.655102$	$979146657/3844$	$1.02504$	$3.87596$	$[0, 0, 0, -95659, -11349030]$	\(y^2=x^3-95659x-11349030\)	2.6.0.a.1, 8.12.0.a.1, 68.12.0-2.a.1.1, 124.12.0.?, 136.24.0.?, $\ldots$	$[ ]$	$1$
143344.m4	143344h1	143344.m	143344h	$4$	$4$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{16} \cdot 17^{6} \cdot 31 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.9	2B	$4216$	$48$	$0$	$1$	$4$	$2$	$1$	$221184$	$1.308529$	$-35937/496$	$0.93090$	$3.28640$	$[0, 0, 0, -3179, -343910]$	\(y^2=x^3-3179x-343910\)	2.3.0.a.1, 4.6.0.c.1, 8.12.0.p.1, 62.6.0.b.1, 68.12.0-4.c.1.1, $\ldots$	$[ ]$	$1$
143344.n1	143344q1	143344.n	143344q	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{6} \cdot 31 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$1$	$1$		$0$	$82944$	$0.616269$	$6912/31$	$0.65713$	$2.57074$	$[0, 0, 0, 289, 4913]$	\(y^2=x^3+289x+4913\)	62.2.0.a.1	$[ ]$	$1$
143344.o1	143344i1	143344.o	143344i	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{3} \cdot 31 \)	$2$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1054$	$2$	$0$	$5.160878632$	$1$		$2$	$16128$	$-0.095116$	$256/31$	$0.67265$	$1.86609$	$[0, 1, 0, 6, -73]$	\(y^2=x^3+x^2+6x-73\)	1054.2.0.?	$[(7, 19), (31/3, 17/3)]$	$1$
143344.p1	143344j1	143344.p	143344j	$2$	$3$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{7} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$6324$	$16$	$0$	$13.94400514$	$1$		$0$	$290304$	$1.346861$	$-71938912000/527$	$0.83482$	$3.77082$	$[0, 1, 0, -63098, -6121705]$	\(y^2=x^3+x^2-63098x-6121705\)	3.4.0.a.1, 204.8.0.?, 372.8.0.?, 1054.2.0.?, 3162.8.0.?, $\ldots$	$[(30021385/252, 133820997715/252)]$	$1$
143344.p2	143344j2	143344.p	143344j	$2$	$3$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{9} \cdot 31^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$6324$	$16$	$0$	$4.648001714$	$1$		$0$	$870912$	$1.896168$	$-11453152000/146363183$	$0.88560$	$3.88044$	$[0, 1, 0, -34198, -11706341]$	\(y^2=x^3+x^2-34198x-11706341\)	3.4.0.a.1, 204.8.0.?, 372.8.0.?, 1054.2.0.?, 3162.8.0.?, $\ldots$	$[(123865/12, 42187931/12)]$	$1$
143344.q1	143344r1	143344.q	143344r	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{9} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1054$	$2$	$0$	$9.801216717$	$1$		$0$	$525312$	$1.470221$	$-19102326016/152303$	$0.89089$	$3.66029$	$[0, 1, 0, -40556, 3151727]$	\(y^2=x^3+x^2-40556x+3151727\)	1054.2.0.?	$[(27949/15, 724393/15)]$	$1$
143344.r1	143344k1	143344.r	143344k	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( 2^{14} \cdot 17^{3} \cdot 31^{2} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.3	2B	$136$	$12$	$0$	$1.359580130$	$1$		$3$	$172032$	$0.938213$	$801765089/3844$	$0.86422$	$3.14324$	$[0, -1, 0, -5264, 148160]$	\(y^2=x^3-x^2-5264x+148160\)	2.3.0.a.1, 8.6.0.e.1, 34.6.0.a.1, 136.12.0.?	$[(58, 186)]$	$1$
143344.r2	143344k2	143344.r	143344k	$2$	$2$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{13} \cdot 17^{3} \cdot 31^{4} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.6.0.3	2B	$136$	$12$	$0$	$2.719160260$	$1$		$3$	$344064$	$1.284786$	$-90518849/1847042$	$0.92434$	$3.26195$	$[0, -1, 0, -2544, 298304]$	\(y^2=x^3-x^2-2544x+298304\)	2.3.0.a.1, 8.6.0.e.1, 68.6.0.c.1, 136.12.0.?	$[(74, 714)]$	$1$
143344.s1	143344s1	143344.s	143344s	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{10} \cdot 31 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$62$	$2$	$0$	$27.09945352$	$1$		$0$	$1363968$	$1.564400$	$2141549312/2589151$	$0.81814$	$3.48202$	$[0, -1, 0, 19556, -1105029]$	\(y^2=x^3-x^2+19556x-1105029\)	62.2.0.a.1	$[(9876671072739/40775, 31045489074273203013/40775)]$	$1$
143344.t1	143344t1	143344.t	143344t	$1$	$1$	\( 2^{4} \cdot 17^{2} \cdot 31 \)	\( - 2^{4} \cdot 17^{7} \cdot 31 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$1054$	$2$	$0$	$1$	$4$	$2$	$0$	$285696$	$0.859119$	$864000/527$	$0.64821$	$2.81657$	$[0, 0, 0, 1445, 4913]$	\(y^2=x^3+1445x+4913\)	1054.2.0.?	$[ ]$	$1$

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